Question

\(\dfrac{3}{3.5}+\dfrac{3}{5.7}+...+\dfrac{3}{47.49}\)

Answer 1

\(=3.\left(\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{47.49}\right)\)

\(=3.\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{47}-\dfrac{1}{49}\right)\)

\(=3.\left(\dfrac{1}{3}-\dfrac{1}{49}\right)\)

\(=3.\dfrac{46}{147}\)

\(=\dfrac{46}{49}\)

Answer 2

\(\dfrac{3}{3.5}+\dfrac{3}{5.7}+...+\dfrac{3}{47.49}\)

=\(\dfrac{3}{2}.\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{47}-\dfrac{1}{49}\right)\)

=\(\dfrac{3}{2}.\left(\dfrac{1}{3}-\dfrac{1}{49}\right)\)

=\(\dfrac{3}{2}.\dfrac{46}{147}\)

=\(\dfrac{23}{49}\)

Answer 3

=3/2.(1/3-1/5+1/5-1/7+...+1/47-1/49)

=3/2.(1/3-1/49)

=3/2.46/147=23/49

Answer 4

\(\dfrac{3}{3.5}+\dfrac{3}{5.7}+...+\dfrac{3}{47.49}\)

= \(\dfrac{3}{2}.\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{47.49}\right)\)

= \(\dfrac{3}{2}.\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{47}-\dfrac{1}{49}\right)\)

= \(\dfrac{3}{2}.\left(\dfrac{1}{3}-\dfrac{1}{49}\right)\) = \(\dfrac{3}{2}.\left(\dfrac{49}{147}-\dfrac{3}{147}\right)\)

= \(\dfrac{3}{2}.\dfrac{46}{147}\)

= \(\dfrac{23}{49}\)